One of the answers for another question of mine recommended using a finishing bit in my router to leave about 1/16" protrusion remaining to be sanded. When I search for "finishing bit" though I can't seem to find anything labeled like that for sale. Is there another term I could look for, or does "finishing bit" just refer to a particular configuration of another bit?
Not sure. We get our flush bits sharpened which takes down the blades which doesn't cut flush anymore.
What you can do is change the bearing to a different diameter.
There are dozens of types of router bits. You are probably looking for a flush cutting or chamfer bit. If you look at a site like Rockler woodworking or just google "types of router bits" you will find many sites with large selections. Even the box stores like Lowes and HD have a decent selection of basic bits.